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DTSTAMP:20180221T222611Z
DTSTART;TZID=America/Los_Angeles:20180223T141000
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SUMMARY:Student Probability/PDE Seminar: Invariant Measures and (Discrete) Nonlinear Schrodinger Equations
UID:115809-ucb-events-calendar@berkeley.edu
ORGANIZER;CN="UC Berkeley Calendar Network":
LOCATION:891 Evans Hall
DESCRIPTION:Kyeongsik Nam\, UC Berkeley\n\nThe notion of invariant measure plays an important role in studying the long-time behavior of solutions to Nonlinear Schrödinger Equations (NLS). For instance\, grand canonical Gibbs measures can be used to prove the almost sure well-posedness of NLS. However\, it is hard to define grand canonical Gibbs measures in high dimensions. One way to remedy this is to use micro-canonical Gibbs measures.This was first considered by Sourav Chatterjee. Since it is not obvious to make sense of micro-canonical Gibbs measures in infinite dimensional function spaces\, we first discretize the space $\\mathbb {R^d}$ and then construct a Gibbs measure on the finite size box. We show that in the mass-subcritical NLS setting\, micro-canonical Gibbs measures get close to solitions as we take an infinite volume limit and then a continuum limit. As a consequence\, we prove the weak version of the soliton resolution conjecture using the ergodic theory.
URL:http://events.berkeley.edu/index.php/calendar/sn/pubaff.html?event_ID=115809&view=preview
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